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Data sparsity is one of the main factors that make word sense disambiguation (WSD) difficult. To overcome this problem we need to find effective ways to use resources other than sense labeled data. In this paper I describe a WSD system that uses a statistical language model based on a large unannotated corpus. The model is used to evaluate the likelihood of various substitutes for a word in a given context. These likelihoods are then used to determine the best sense for the word in novel contexts. The resulting system participated in three tasks in the SemEval 2007 workshop. The WSD of prepositions task proved to be challenging for the system, possibly illustrating some of its limitations: e.g. not all words have good substitutes. The system achieved promising results for the English lexical sample and English lexical substitution tasks.